The short version is that if the language you speak requires different verbs for the present and the future, it causes you to think about it differently. Depending on the magnitude of the effect, this has important implications for construal level theory. If your language allows you to think about the future in Near mode, it may allow you to think about it more rationally.

"The Chomskyan school also holds the belief that linguistic structures are largely innate and that what are perceived as differences between specific languages – the knowledge acquired by learning a language – are merely surface phenomena and do not affect cognitive processes that are universal to all human beings. This theory became the dominant paradigm in American linguistics from the 1960s through the 1980s and the notion of linguistic relativity fell out of favor and became even the object of ridicule."

I realize that this was an introductory video to their theory and initial findings, but failing to make any acknowledgement of the fact that correlation doesn't imply causation doesn't seem very rigorous of them. The previous discussion linked to in the OP has a quotation from Geoff Pullum (via roshni) which makes the same point, and then some. I was going type up the same objection to shoehorning languages into "weak FTR" and "strong FTR" boxes myself, but the quotation makes the point better than I could have. I'll repost the quotation here for ease of reference:

If English has future tense markers at all, it has at least a dozen of different ones; but simple use of the present tense is a very prominent way of referring to future time, so what do we make of that? For my part, I have no confidence at all that English is accurately described as "strong FTR". Nearly all traditional grammarians report English as having a tense system that includes a future tense, but that isn't really true; will is a modal auxiliary that has various other uses too. If the facts are shaky for English, how likely are they to be accurate on languages that have not been studied nearly so intensively?

I also worry that it is too easy to find correlations of this kind, and we don't have any idea just how easy until a concerted effort has been made to show that the spurious ones are not supportable. For example, if we took "has (vs. does not have) pharyngeal consonants", or "uses (vs. does not use) close front rounded vowels", would we find correlations there too? I have some colleagues here at the University of Edinburgh, within Simon Kirby's research group, who have run some informal experiments on the data Chen uses to see if dredging up spurious correlations of this kind is easy or hard, and so far they have found it jaw-droppingly easy. (I won't say any more, because I am in the weird position of writing unrefereed telegraphing of unrefereed and informal objections to an unrefereed and unpublished working paper, and it's all getting a bit too weird for me.)

Observing a correlation between the dominant language in a country and the saving habits of that country is well and good, but how, exactly, do they intend to control for cultural differences? How will their theories account for multilingualism or the non-native speakers of a given language in a country, particularly if they form a significant part of the population? How about economic inequality in a given country, what kind of role does that play in saving habits?

I'm not convinced. There are good reasons why strong linguistic relativity has been objected to as vehemently as it has.

Grammatical gender can have weak priming effects. eg. if your language codes "bridge" as masculine, you're more likely to describe one using words like "stout" and "strong", as opposed to languages with feminine bridges that are likely to be "graceful" or "soaring". If I recall correctly she also did some similar work with the way languages encode path and manner of movement (ie. in English I would say "he ran out of the room", while in French it's more like "he left the room running").

There's also a bunch of other related findings. eg. people generally conceptualise time/logical progressions as going in the same direction as their writing system, Russian speakers are faster to distinguish between light and dark blue than English speakers because in Russian they're two distinct colours, that sort of thing.

I'm still on the fence about this Keith Chen stuff. Most of those tasks I just described involve verbal labelling/categorisation, so it's not surprising to me that when you're explicitly asked to come up with words for things you would be primed by what kind of words and structures your language has. Thinking about the future seems less language-dependent than that.

I've no problem stomaching these findings; I have no objections to weak priming effects, differences in ease or speed of categorization and the like, and it doesn't seem like Boroditsky is pushing a case for anything more. It's strong relativism that I have misgivings about (as well as, in this case, the way the folks in the video seem to have overlooked controlling for factors other than the linguistic ones).

Well yeah, strong relativism is a steaming pile of nonsense. But I'm not sure that you need strong relativism to get future-oriented behaviour differences, weak priming effects could well add up over time to produce noticeable differences in amount of savings over a long period.

What kind of factors did you have in mind? As far as I know they controlled for country, city, religion, income, family values.. probably some other stuff I can't remember. And at least some of the pairs of households he compared were in non-Western countries, again I can't remember off the top of my head.

I agree that less-than-strong forms of relativism can have an effect; priming effects are well enough known that it would be downright weird if human language was somehow exempt. But, again, this comes down to the non-linguistic factors, and distinguishing their effects from the effects of linguistic priming.

I can't address the specifics of how well they conducted their study - it's something of a black box to me. However, the graph around 8:15 in the video shows some seriously wonky stuff that I will flat-out refuse to accept as properly controlled for measuring the effect of linguistic priming. Consider, for example, the fact that the average Swedish saving rate is ~24% , while in Norway they save ~32%, when we could be having the argument whether they even have separate languages (mutual intelligibility, etc.). Compare the various English-speaking countries, such as Canada and the US: extremely similar culturally and linguistically, yet we get differences. If they had really managed to set up the study so perfectly that language was the only variable, we shouldn't be getting differences, or certainly not ones this salient.

Some country/language pairs do match up nicely; Sweden and Denmark are almost identical, and the same goes for the US and the UK. But the shortcomings of the graph call the whole thing into question; based on what I'm seeing, I don't trust Chen et al. to be able to extract the linguistic differences from all the other factors. They've gone wrong somewhere, even if it's impossible to say exactly where and exactly how much just by watching the video.